When the car engine warms up it will just shut down while driving. Once it cools down it will start up again but does the same thing. I was told it was the fuel regulator, is this right? Is there another name for that part?

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Jamiem is correct. If you have recently done work on your coolant system you will need to bleed the system. While the engine is cool, remove the radiator cap and start the engine. (do not do this with a hot engine!) As the engine warms up, the coolant level should drop twice. Each time it drops fill the coolant up again in the radiator. Once the engine has warmed up and your radiator is full shut it off and let it cool down. Replace the cap, let it warm up again and test the heat again.

Other things to check if this does not fix it is the heater control valve, the fuses (as mentioned, though I think you'd know if your blower motor wasn't working) and finally and hopefully not, the heater core itself.

your ignition coil are going bad, they need to be replaced. once the car gets hot the circuit shut down the car when hot. once they cool your riding again until they get hot. thats your problem. Good Luck

give the engine a minute or two to cool down before turning it off. This cool down period allows oil to circulate and cool down the bearings in the turbo. If you shut off the engine immediately after hard driving, the oil can gum up around the hot bearings and create problems down the road.
Hope this helps

Well, something idoesnt like to be warm in it, ive seen this caused by multiple things, but most commonly its the starter going out it gets warm from the engine running and the brushes expand and short, cools off brushes shrink and VOla Vrooom Vroom!